TSTP Solution File: SYN719-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN719-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:35:50 EDT 2023
% Result : Unsatisfiable 2.11s 0.93s
% Output : Proof 2.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYN719-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.35 % Computer : n026.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Aug 26 18:19:03 EDT 2023
% 0.12/0.35 % CPUTime :
% 2.11/0.93 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.11/0.93
% 2.11/0.93 % SZS status Unsatisfiable
% 2.11/0.94
% 2.11/0.95 % SZS output start Proof
% 2.11/0.95 Take the following subset of the input axioms:
% 2.11/0.95 fof(not_p68_46, negated_conjecture, ~p68(f19(f21(c83, c77), c79), c81)).
% 2.11/0.95 fof(p14_38, negated_conjecture, ![X13]: p14(X13, X13)).
% 2.11/0.95 fof(p14_45, negated_conjecture, ![X20]: p14(f23(f26(c84, c85), X20), X20)).
% 2.11/0.95 fof(p14_90, negated_conjecture, ![X14, X15, X13_2]: (p14(X14, X15) | (~p14(X13_2, X14) | ~p14(X13_2, X15)))).
% 2.11/0.95 fof(p66_41, negated_conjecture, p66(f12(c78, c77), c79)).
% 2.11/0.95 fof(p67_42, negated_conjecture, p67(f16(c80, c81), c82)).
% 2.11/0.95 fof(p68_126, negated_conjecture, ![X221, X222, X224, X223]: (p68(f19(f21(c83, c77), X221), X222) | (~p67(f16(c80, X224), c82) | (~p66(f12(c78, c77), X221) | (~p14(X222, f23(f26(c84, X223), X224)) | ~p69(f36(c86, f38(X223, f40(f42(f44(f46(c87, X221), X222), X223), X224))), f30(c88, f32(c89, f8(c75, c76))))))))).
% 2.11/0.95 fof(p69_52, negated_conjecture, ![X230, X229]: (p69(f36(c86, X229), X230) | ~p70(X230, X229))).
% 2.11/0.95 fof(p70_43, negated_conjecture, ![X242, X243]: p70(f30(c88, X242), f38(c85, X243))).
% 2.11/0.95
% 2.11/0.95 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.11/0.95 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.11/0.95 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.11/0.95 fresh(y, y, x1...xn) = u
% 2.11/0.95 C => fresh(s, t, x1...xn) = v
% 2.11/0.95 where fresh is a fresh function symbol and x1..xn are the free
% 2.11/0.95 variables of u and v.
% 2.11/0.95 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.11/0.95 input problem has no model of domain size 1).
% 2.11/0.95
% 2.11/0.95 The encoding turns the above axioms into the following unit equations and goals:
% 2.11/0.95
% 2.11/0.95 Axiom 1 (p14_38): p14(X, X) = true.
% 2.11/0.95 Axiom 2 (p67_42): p67(f16(c80, c81), c82) = true.
% 2.11/0.95 Axiom 3 (p66_41): p66(f12(c78, c77), c79) = true.
% 2.11/0.95 Axiom 4 (p68_126): fresh147(X, X, Y, Z) = true.
% 2.11/0.95 Axiom 5 (p14_90): fresh132(X, X, Y, Z) = true.
% 2.11/0.95 Axiom 6 (p69_52): fresh19(X, X, Y, Z) = true.
% 2.11/0.95 Axiom 7 (p14_90): fresh133(X, X, Y, Z, W) = p14(Y, Z).
% 2.11/0.95 Axiom 8 (p14_45): p14(f23(f26(c84, c85), X), X) = true.
% 2.11/0.95 Axiom 9 (p70_43): p70(f30(c88, X), f38(c85, Y)) = true.
% 2.11/0.95 Axiom 10 (p68_126): fresh145(X, X, Y, Z, W, V) = p68(f19(f21(c83, c77), Y), Z).
% 2.11/0.95 Axiom 11 (p69_52): fresh19(p70(X, Y), true, Y, X) = p69(f36(c86, Y), X).
% 2.11/0.95 Axiom 12 (p14_90): fresh133(p14(X, Y), true, Z, Y, X) = fresh132(p14(X, Z), true, Z, Y).
% 2.11/0.95 Axiom 13 (p68_126): fresh146(X, X, Y, Z, W, V) = fresh147(p14(Z, f23(f26(c84, V), W)), true, Y, Z).
% 2.11/0.95 Axiom 14 (p68_126): fresh144(X, X, Y, Z, W, V) = fresh145(p66(f12(c78, c77), Y), true, Y, Z, W, V).
% 2.11/0.95 Axiom 15 (p68_126): fresh144(p69(f36(c86, f38(X, f40(f42(f44(f46(c87, Y), Z), X), W))), f30(c88, f32(c89, f8(c75, c76)))), true, Y, Z, W, X) = fresh146(p67(f16(c80, W), c82), true, Y, Z, W, X).
% 2.11/0.95
% 2.11/0.95 Goal 1 (not_p68_46): p68(f19(f21(c83, c77), c79), c81) = true.
% 2.11/0.95 Proof:
% 2.11/0.96 p68(f19(f21(c83, c77), c79), c81)
% 2.11/0.96 = { by axiom 10 (p68_126) R->L }
% 2.11/0.96 fresh145(true, true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 3 (p66_41) R->L }
% 2.11/0.96 fresh145(p66(f12(c78, c77), c79), true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 14 (p68_126) R->L }
% 2.11/0.96 fresh144(true, true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 6 (p69_52) R->L }
% 2.11/0.96 fresh144(fresh19(true, true, f38(c85, f40(f42(f44(f46(c87, c79), c81), c85), c81)), f30(c88, f32(c89, f8(c75, c76)))), true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 9 (p70_43) R->L }
% 2.11/0.96 fresh144(fresh19(p70(f30(c88, f32(c89, f8(c75, c76))), f38(c85, f40(f42(f44(f46(c87, c79), c81), c85), c81))), true, f38(c85, f40(f42(f44(f46(c87, c79), c81), c85), c81)), f30(c88, f32(c89, f8(c75, c76)))), true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 11 (p69_52) }
% 2.11/0.96 fresh144(p69(f36(c86, f38(c85, f40(f42(f44(f46(c87, c79), c81), c85), c81))), f30(c88, f32(c89, f8(c75, c76)))), true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 15 (p68_126) }
% 2.11/0.96 fresh146(p67(f16(c80, c81), c82), true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 2 (p67_42) }
% 2.11/0.96 fresh146(true, true, c79, c81, c81, c85)
% 2.11/0.96 = { by axiom 13 (p68_126) }
% 2.11/0.96 fresh147(p14(c81, f23(f26(c84, c85), c81)), true, c79, c81)
% 2.11/0.96 = { by axiom 7 (p14_90) R->L }
% 2.11/0.96 fresh147(fresh133(true, true, c81, f23(f26(c84, c85), c81), f23(f26(c84, c85), c81)), true, c79, c81)
% 2.11/0.96 = { by axiom 1 (p14_38) R->L }
% 2.11/0.96 fresh147(fresh133(p14(f23(f26(c84, c85), c81), f23(f26(c84, c85), c81)), true, c81, f23(f26(c84, c85), c81), f23(f26(c84, c85), c81)), true, c79, c81)
% 2.11/0.96 = { by axiom 12 (p14_90) }
% 2.11/0.96 fresh147(fresh132(p14(f23(f26(c84, c85), c81), c81), true, c81, f23(f26(c84, c85), c81)), true, c79, c81)
% 2.11/0.96 = { by axiom 8 (p14_45) }
% 2.11/0.96 fresh147(fresh132(true, true, c81, f23(f26(c84, c85), c81)), true, c79, c81)
% 2.11/0.96 = { by axiom 5 (p14_90) }
% 2.11/0.96 fresh147(true, true, c79, c81)
% 2.11/0.96 = { by axiom 4 (p68_126) }
% 2.11/0.96 true
% 2.11/0.96 % SZS output end Proof
% 2.11/0.96
% 2.11/0.96 RESULT: Unsatisfiable (the axioms are contradictory).
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